Asked by Michael Clifford on May 09, 2024
Verified
Find all of the square roots of the perfect square 49 \frac{4}{9} 94 .
A) 23 \frac{2}{3} 32
B) ±827\pm \frac { 8 } { 27 }±278
C) 12\frac { 1 } { 2 }21
D) ±23\pm \frac { 2 } { 3 }±32
E) ±34\pm \frac { 3 } { 4 }±43
Square Roots
The value that, when multiplied by itself, gives the original number, often denoted as √x.
Perfect Square
A number that is the square of an integer, such as 1, 4, 9, 16, etc.
Evaluate
To figure out the valuation of an expression.
- Identify the characteristics of square roots and cube roots for specific numbers.
Verified Answer
CS
Courtney SandersMay 12, 2024
Final Answer :
D
Explanation :
The square root of a perfect square, in this case, 49 \frac{4}{9} 94 , includes both the positive and negative roots because squaring either will return the original value. The square root of 49 \frac{4}{9} 94 is 23 \frac{2}{3} 32 , so both 23 \frac{2}{3} 32 and −23 -\frac{2}{3} −32 are correct, making option D the correct answer.
Learning Objectives
- Identify the characteristics of square roots and cube roots for specific numbers.